We study several enumerative properties of the set of all circular binary strings without zigzags and of the set of all (0, 1)-necklaces without zigzags, where a zigzag is a 1 followed and preceded by a 0 or a 0 followed and preceded by a 1.

Abstract Postnikov constructed a cellular decomposition of the totally nonnegative Grassmannians. The poset cells can be described (in particular) via Grassmann necklaces. We study certain quiver Grassmannians for cyclic admitting decomposition, whose are naturally labeled by show that posets coincide with reversed cell investigate algebro-geometric and combinatorial properties these In particu...

We give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the lp norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p = 1, p even, and p = ∞. F...